周期性边界条件、间断点及第二类边界条件的数值处理

应用有限元方法求解流体力学、传热学以及其它的工程问题,一般讲,所得方程组的系数矩阵具有对称性。当方程组中某两个待定变量具有Q_i=Q_i G的约束条件时(这里Q_i和Q_i分别是第i个和第j个待求的变量,G是某一常量),可以使用本文提出的数学处理方法,使原对称、正定方程组在解除上述形式约束后,得到的新方程组仍保持对称的性质。文章证明了数学处理的合理性,并据此编制了ALGOL程序。

The Numerical Method for Periodical Condition, Noncontinuous Point and Second Boundary Condition

Generally, the coefficient matrix of equation system is symmetric white the finite element method is used for questions on fluid dynamics, heat transfer and other engineering subjects. If there is a restrictive condition with the form of Q_i=Q_i G, where Q_i and Q_i are respectively the ith and jth variables of equation system, G is a constant. The methematical treatment method provided in this paper can be used to make the original equation system with symmetrical and positive definite quality to be a new equation system with symmetric quality after relieving the restrictive condition mentioned above. The mathematical treatment has been justified in this paper and an ALGOL computational program is compiled.